Simplify the expression. $(-k^{4}+6k^{3}+6k)(3k^{4}+3k^{2})$
Answer: First use the distributive property. $ - k^4 (3 k^4) - k^4 (3 k^2) + 6 k^3 (3 k^4) + 6 k^3 (3 k^2) + 6 k (3 k^4) + 6 k (3 k^2) $ Simplify. $ - 3k^{8} - 3k^{6} + 18k^{7} + 18k^{5} + 18k^{5} + 18k^{3} $ $-3k^{8}+18k^{7}-3k^{6}+36k^{5}+18k^{3}$ Identify like terms. $ {- 3k^{8}} {- 3k^{6}} {+ 18k^{7}} {+ 18k^{5}} {+ 18k^{5}} {+ 18k^{3}} $ Add the coefficients. $ { -3k^{8}} {+ 18k^{7}} { -3k^{6}} {+ 36k^{5}} {+ 18k^{3}} $